Part one the egg
The egg's journey starts well before conception, and well before you thought about trying to conceive, or even met the man you want to have a baby with. The follicles of immature eggs form in a female's ovaries while she is still in her own mother's uterus. All girls are born with all the egg's they will ever have (though science may change that at some point in the not-too-distant future). At birth, girls have around 400,000 follicles. Usually, one egg is released per menstrual cycle once a female starts having periods and commences ovulating (which doesn't have to happen at the same time ovulation can start several years after menarche). No, you won't have 400,000 menstrual cycles during which you also ovulate. Not all follicles mature to be released at ovulation, and several hundreds of follicles may go to waste during any one cycle. RIP.
Follicle Stimulating Hormone (FSH for short) causes a few follicles to mature during each cycle. The follicles produce estrogen, and the uterus starts getting ready for a fertilized egg by producing a nice and cushy environment in which said egg can implant. Eggs that are released are triggered by a different hormone called Luteinizing Hormone, or LH. This is the same hormone that also allows you to figure out when you ovulate if you use ovulation tests. Whether you use ovulation tests or not, an egg that is released from one of the ovaries (yes, usually only one) will be sucked into the fallopian tubes, where it will quickly meet with sperm if you've had intercourse in the last five or so days. If you have intercourse during your ovulation, the egg and sperm will meet closer to the uterine end of the fallopian tube in question.
Sperm meets egg
If you thought being born with 400,000 immature follicles was impressive, the male end of the story will make you faint. Men can eject (or was that ejaculate?) as many as 250 MILLION every time they climax. The male gametes are not only much more abundant; they are also an awful lot faster. As a bonus, they also live longer. Sperm can reach the fallopian tubes in a matter of hours. A fallopian tube is only a few inches long, but the ovum can take up to five days traveling down there to get to the uterus (if fertilized, otherwise it perishes).
Only one sperm will be lucky enough to win the grand race to the egg, and being shaped properly, as well as having the speed necessary, counts in this game. Not all sperm make it to the fallopian tubes. Out of all those millions, only a couple of hundred will get to the egg at all. Sperm can stick around the female reproductive tract for around five days. Some scientists say up to seven. Those swimmers will have the advantage if they were already there by the time the egg is released.
Eggs that are not fertilized are reabsorbed by the female body. After that, your hormones will go back to normal, and you will get your period, during which all that uterine lining that was built up to host your theoretical fertilzed egg is flushed out. Some of that reabsorbs too, mind you. Along with part of your uterine lining, some of your iron stores may be expelled too. If you're prone to anemia, take a supplement. If an egg is fertilized by a sperm, it changes its structure right away so no other sperm can get inside.
Once the egg and sperm get together and form one cell, it is called a zygote. The zygote continues the process of cell division all the time, though it doesn't actually get bigger during this time. On day five, the zygote graduates to become a blastocyst, by which time it will also have reached the uterus ready to implant and slowly develop to become a real baby.